The Jumping Frog Problem

The Jumping Frog Problem in an open-ended problem-solving unit for use ideally in small groups of students. The Problem can be posed in various ways, but the basic idea is that students are challenged to think about the mechanics by which a frog executes a jump. Perspectives from physics, biology and chemistry are interconnected in a scenario where students can generate informed opinion about the anatomy and physiology of a frog's jump.

Encourage your students to think about this problem from various angles - the effects of bone length and density, the effects of muscle type and size, the role of ATP, behavioral stimuli and jumping, etc.

Here we have posed the Problem as a design problem. There are special ethical concerns surrounding this approach, and these should be used to encourage students to begin or continue developing their sense of bioethics. Find a time to discuss bioethical issues with your students, especially in the context of current issues in this area - for example, cloning.

Sample outline of a Jumping Frog Lesson:

1. Introduce the Problem: Students are to design a frog to win a contest, such as the Calaveras County Frog Jumping Contest. Possible ideas for a scenario include:
• Eccentric millionaire has offered massive dollar prize to the winner.
• Department of Defense has initiated a program to design a "super soldier," but has decided to start experimentation on frogs, so it is using the contest as a way of deciding which biotech company (composed of student teams) to use. (A variation on this is that student teams were working on super soldier project before funding was cut abruptly, so they are now trying to apply the technology to the contest and bet money on it so they can continue funding their project.)
• Conservation group has decided that one way to save the frogs is to make them more "visible / valuable" to draw attention to the frogs' plight. They are willing to modify one to save the others. Alternately, frogs are being wiped out by dogs or some other human-introduced predator, so an eco-group has decided to start breeding or genetically-altering the frogs to make them faster so they can escape this new predator.
• Racehorse breeder has hired students to do research on increasing bone length and muscle size and/or composition in order to develop a faster horse. The breeder has them working on frogs because 1) they are a lot cheaper than horses and 2) they are easier to grow and manipulate (cloning of frogs has been done for many years now). The breeder has chosen the Calaveras County contest because it is the closest thing in the frog world to a horse race, emphasizing similar traits.
2. Have students go to Habitat Land where they research the different types of frogs and choose which breed they want to use and why.
• Students could fill out a matrix about each frog and its environment, reproductive habits, predator prey relationships, etc. then explain which frog type they are going to use.
• Students could do a mini report about their chosen frog and why it is the best frog for the problem.
• Students could do a concept map about all/chosen frog species, and explain their choice.
3. Students go to the organ hut and do an overview of the different organ systems so they can identify which systems would be best to focus on (ie, muscles and bones).
• students might fill out the worksheet that guides them through the resources in the organ hut, and answer questions at the end about their thoughts as to which systems play more or less important roles in locomotion and why.
4. Students go to the bone hut and start to learn the names of the major bones in the frog, to facilitate their discussion about the role(s) of these in jumping.
• Students would then fill out a diagram of a human skeleton that had arrows to bones with identical names as frog's, to allow them to make connections between the two skeletal systems.
• Students would then compare human skeleton (with all labels) to frog skeleton and compare and contrast.
• Students could do a worksheet that had questions or a table about identical features, similar features, and dissimilar features. You might have them work on the Venn diagram activity for this objective. Encourage students to think about why they think those differences exist.
5. Students return to the bone hut and study internal (and perhaps microscopic) structure of bone.
• Have students work on the hollow bones demo, so they gain an understanding of the tradeoff between support and weight in the structure of bone. That is, less "hollow" bones might support more weight, but would also be heavier. Students should be thinking of the implications of this finding for the Jumping Frog Problem.
• Students could do a lab examining the structure of bone by taking some chicken bones and soaking them for a few days in water, vinegar, bleach, etc. and see what happens to the bones (acid removes calcium and bones become very flexible). Ask students questions about whether they want high / low calcium in their frog and why. (High calcium makes for stiffer levers, can take more weight; low calcium makes for more flexible levers, perhaps could store more elastic potential energy and withstand greater impact because they are less brittle.)
6. Students go to muscle hut and start to study muscles.
• Students would fill out worksheet about different muscle types (skeletal, cardiac, smooth) and decide which affects locomotion the most.
• Students would learn names / classifications of skeletal muscles, to facilitate discussion.
• You might have students color a coded diagram of frog muscles with the different muscle types, such as are available in the Zoology Coloring Book.
• Students would learn about the different types of skeletal muscles (fast / intermediate / slow twitch). Have students experiment with this by working through the Java Race. They should be reaching conclusions about which kind of skeletal muscle works best for a jump.
• They could complete a table comparing the different characteristics of the three types of skeletal muscle.

Extensions

1. More advanced students could learn about sarcomeres and extension / flexion of muscle. This information is in the muscle hut.
2. Have students do a lever lab to determine relationship between length of bone and where the muscle attaches with regards to the amount of force generated.
• Students could do a lever lab in their classroom where they learn that mechanical advantage (amount that a lever multiplies your force or your speed) is length of the effort arm divided by the resistance arm. Advantage of doing this using a program like Interactive Physics is that it would be easier to simulate a series of interconnected levers like legs and see how they affect distance of jump, especially since the muscles may act in some ways like pulleys.
3. Have students play the Java Frog game to figure out what the best ballistic angle would be.
• Student would complete a worksheet that would lead them to understand why frogs jump and why they may not like to jump, plus reasons for the particular nuances of this game (like additional lives makes it more likely that the predating bird will show up.)

Student Exhibitions

7. Students then decide which muscles and bones to increase / decrease / alter.
• Students would write a report stating their hypothesis about which parts to modify and why. They would describe the frog's ecology and compare its original morphology to its new shape and explain their reasoning for their changes and choices (like species, etc.). They could also go further and analyze what effects these changes might have if their modified frog is released to the wild. This report could even be a summary of everything they've learned, incorporating or replacing many of the earlier worksheets and assignments.
• Students could make and present a poster that shows old and new frog, and conveys much of the information of the above lab report.
• Students could make a hypercard (or similar) stack with information about their frog, again incorporating information from above, perhaps using a morph or Goo program to create before and after pictures of their frog.

Extension

1. Students might go to bioethics hut and read about breeding and genetic manipulation of animals, along with pro and con essays. They could also find out about what is going on with frog environments, etc.
• Have students conduct internet searches on current issues in bioethics.
• Either as a separate paper or as part of the above report, students would summarize positions for and against animal manipulation and take a stand on the general topic and about their particular situation.
• Students could do small group or whole-class debates.
• Students could design a poster for elementary students that illuminates a set of issues and different positions.
• Students could write newspaper columns about the "contest" and also do an editorial.